Sleep and wake in a model of the thalamocortical system with Martinotti cells

Abstract

The mechanisms leading to the alternation between active (UP) and silent (DOWN) states during sleep slow waves (SWs) remain poorly understood. Previous models have explained the transition to the DOWN state by a progressive failure of excitation because of the build-up of adaptation currents or synaptic depression. However, these models are at odds with recent studies suggesting a role for presynaptic inhibition by Martinotti cells (MaCs) in generating SWs. Here, we update a classical large-scale model of sleep SWs to include MaCs and propose a different mechanism for the generation of SWs. In the wake mode, the network exhibits irregular and selective activity with low firing rates (FRs). Following an increase in the strength of background inputs and a modulation of synaptic strength and potassium leak potential mimicking the reduced effect of acetylcholine during sleep, the network enters a sleep-like regime in which local increases of network activity trigger bursts of MaC activity, resulting in strong disfacilitation of the local network via presynaptic GABA_B1a -type inhibition. This model replicates findings on slow wave activity (SWA) during sleep that challenge previous models, including low and skewed FRs that are comparable between the wake and sleep modes, higher synchrony of transitions to DOWN states than to UP states, the possibility of triggering SWs by optogenetic stimulation of MaCs, and the local dependence of SWA on synaptic strength. Overall, this work points to a role for presynaptic inhibition by MaCs in the generation of DOWN states during sleep.

Keywords: Martinotti cells; computational model; large-scale simulation; sleep; slow wave; somatostatin-positive cells; visual cortex; wake.

Fig 1.. Model architecture.

Schematic of the thalamocortical model. Primary thalamocortical circuit (middle) including a 3-layered primary visual cortical area, the reticular nucleus (R), and the lateral geniculate nucleus of the thalamus (T). Each cortical layer contains vertically (blue) and horizontally (red) selective populations of Pyramidal (PyC, black) and Basket (BaC, white) cells. The deep layer (L56) additionally contains vertically and horizontally selective populations of Martinotti cells (MaC, green). Visual inputs, including spontaneous random optic nerve firing, excite inhibitory (light grey) and excitatory (dark grey) neurons in T. Background cortical firing excites all cortical PyCs and BaCs through AMPA, NMDA and mGluR. A: Intracortical horizontal (intralaminar) connections: PyCs and BaCs from each layer form connections within this layer, preferentially with units sharing the same selectivity (shown only for the superficial layer, L23). B: Connections to and from MaCs: MaCs are connected by electrical synapses. They receive excitatory and inhibitory connections from PyCs and BaCs from all layers, with stronger excitatory inputs from iso-orientation PyCs, and inhibit them in return (shown only for L56). C: Intracortical vertical (interlaminar) connections: columnar focused excitatory projections among units with the same selectivity are made from L4 to L23, from L23 to L56, and from L56 back to L4 and L23. GABA_B-like connections are made from L23 BaCs (double-bouquet cell analogs) to iso-orientation PyCs within a narrow column (shown only for horizontally selective units). D: Intrathalamic connections: Reticular neurons form an inhibitory network that sends diffuse inhibitory projections to T. Thalamocortical units are inhibited by local interneurons, and form collaterals onto R en route to the cortex. E: Thalamocortical loops: Thalamocortical neurons project to both excitatory and inhibitory cells in L4 and L56. Orientation selectivity is achieved by the convergence of afferents from an oriented rectangular region in T onto individual PyCs in L4 and L56. Thalamocortical projections onto BaCs follow a Gaussian kernel. Feedback cortico-thalamic connections from L56 PyCs target all thalamic units. Not drawn to scale.

Fig 2.. Spontaneous and evoked activity in the wake mode.

A-: Network activity within 1 s of the presentation of a full-field vertical grating stimulus. A-1: Spike histogram of cortical units with vertical (top) and horizontal (bottom) selectivity. A-2: Membrane potential rasters displaying activity for a random subset of vertically selective L4 PyCs (top), L4 BaCs (middle) and MaCs (bottom) A-3: Local field potential (LFP) computed from the conductances of all PyCs. A-4: Membrane potential traces for representative vertically selective units. Red vertical lines show spikes. Top, Middle: L4 PyC and BaC. Bottom: MaC. Note the periodic increase and suppression of PyCs activity depending on the phase of the grating in its receptive field. B: Time-averaged topographic representation of the membrane potential for L4 PyCs of different orientation selectivity in the spontaneous and evoked conditions. We average 20 msec of activity, 500msec before or 50 msec after stimulus presentation for the spontaneous and grating conditions, respectively. The vertically selective population responds preferentially to the vertical grating. C: Peristimulus time histogram showing instantaneous arithmetic firing rate for all populations, split by neuron type, layer and selectivity. We average activity of units within the vertical slice represented by the black rectangle in B over N = 30 stimulus presentations. Note the greater increase in activity at the active phase of the grating for vertically selective units than for horizontally selective units, and the recruitment of vertically selective following stimulus presentation. D-: Boxplots of spontaneous and evoked unit firing rates, split by population, for units within the vertical slice represented in B. Only vertically selective units are shown. We average over N = 30 trials the activity for the first 100 msec following stimulus presentation (grating) or 1 s preceding stimulus presentation (spontaneous). Note the sparseness and low rates of spontaneous activity, and the increase in activity following grating presentation. MaCs are mostly silent during the first 100 msec following stimulus presentation (see subplot D).

Fig 3.. Slow waves in the sleep mode.

A-: Overall network activity during 20 s of simulation in the sleep mode. A-1: Spike histogram for all cortical units. A-2: Membrane potential raster for different populations as in Fig 2. Note the burstiness of MaCs activity and the periods of network hyperpolarization. A-3: LFP computed from the conductances of all PyCs. The LFP shows high amplitude slow oscillations with positive peaks corresponding to periods of network hyperpolarization. A-4: Single unit membrane potential for different units as in Fig 2. C: Time-averaged topographic representation of the membrane potential for L4 vertically selective PyCs. 20 msec of activity was averaged at three time points of interest (vertical bars on the LFP): (T1) a period of overall depolarized activity (UP state); (T2) a local DOWN state; (T3) a DOWN state synchronized over the network. The red square represents the “local subnetwork” used throughout and the dotted circle shows the maximal extent of MaC-to-PyC connections.

Fig 4.. Comparison of activity in the wake and sleep modes.

A: Center: Scatter plot of firing rates for simulations in the spontaneous wake and sleep modes, for a random sample of PyCs and BaCs. Rates are displayed on a symmetric log scale. Unit firing rates are similar during wake and sleep (R = 0.80 for BaC, R = 0.90 for PyC). Top and right: Distribution of firing rates in the sleep and wake modes. The distributions are similar in the two states. BaC firing rates are approximately log-normally distributed. PyC firing rates are low and highly skewed. B: Distribution of amplitudes for all the positive peaks of the low-pass filtered LFP in the sleep and wake modes (with or without stimulus presentation). The distribution of amplitudes in the sleep mode is highly dispersed compared to the spontaneous wake distribution. The dispersion of the distribution reflects the irregularity of slow activity in the sleep mode. The vertical bar indicates the arbitrary conservative threshold used throughout for slow wave detection (99^th percentile of the amplitude distribution in the wake mode with stimuli). C: LFP for the sleep and spontaneous wake conditions. The high amplitude and irregular slow deflections (0.5–2 Hz) are mostly absent in the wake mode. D: Inhibitory to excitatory ratio (I-E, left) and main excitatory and inhibitory conductances (right) and during wake, active periods of sleep (UP) and silent periods of sleep (DOWN).

Fig 5.. A key role for GABA_B1a activity mediated by Martinotti cells in the generation of slow waves.

Activity of units within the local subnetwork depicted in Fig 3C, time-locked to the start of the waves detected from the LFP of the subnetwork (N = 94). A: Mean ± standard deviation across waves of the subnetwork’s LFP. B: Instantaneous population arithmetic firing rate, averaged across waves, for all populations. Note the increase in PyCs and BaCs activity, followed by a burst of MaCs activity, before network silencing. C: Population average of excitatory (AMPA and NMDA) and GABA_A conductances for L4 PyCs. D: Bottom: Scatter plot of weights (reflecting short-term synaptic dynamics) for a random sample of spikes from PyCs to MaCs (left, facilitating short-term dynamics) and from BaCs to MaCs (right, depressing short-term dynamics). Red curve is a LOWESS fit (frac = 0.2, delta = 1.0) showing a decrease in average weights for spikes from BaCs. Top: Weighted sum of spikes representing the total excitatory (left) and inhibitory (right) synaptic barrages onto MaCs. The increase in PyCs and BaCs firing rate combined with the short-term dynamics of excitatory and inhibitory connections onto MaCs leads to a tipping of the I-E balance of MaC inputs in favor of excitation, and the recruitment of MaCs. E: Median, 25^th and 75^th percentiles over all waves and all PyCs and BaCs of the instantaneous GABA_B1a conductance. The burst in MaC activity leads to strong presynaptic inhibition in most units and explains the network’s silencing. F: SWA and network firing rate during 30 sec simulations, varying the GABA_B1a peak conductance from the parameter region depicted in figure 6. An increase in GABA_B1a-type inhibition leads to a deepening of network hyperpolarizations and greater SWA.

Fig 6.. Effects of parameter changes mimicking neuromodulation on network activity.

A: SWA (0.5–2 Hz power) for 30 sec simulations with different scaling of PyCs and BaCs AMPA weight amplitudes (${{\mathrm{g}}_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}}_{\mathrm{A}\mathrm{M}\mathrm{P}\mathrm{A}}$) and potassium leak conductance (g_KL) relative to their value in the wake mode. Other wake-to-sleep parameter changes are kept constant. Smallest circles indicate that the average L4 PyC FR is below 0.2 Hz, the average L4 BaC FR is below 5 Hz, or the first quartile of membrane potentials is above −64 mV (indicating of an absence of prolonged DOWN states). Red triangles indicate the parameter region used from which we varied other investigated parameters of interest. B: 15 s heatmap of membrane potentials of L4 PyCs for illustrative parameter combinations.

Fig 7.. UP to DOWN transitions are more synchronous than DOWN to UP transitions.

We assessed the synchrony of transitions to and from hyperpolarization across the 50% largest slow waves detected during a 120 s recording in the sleep mode for units within the local region depicted in Fig 3–C. A: Filtered LFP of an example wave. Network hyperpolarization corresponds to the positive peak. The points of interest used for constraining the period in which the UP to DOWN (U-D) and DOWN to UP (D-U) transitions are searched for are indicated with red stars (start of wave, positive peak, end of wave). The U-D and D-U periods are indicated with vertical bars. B: Smoothed membrane potential of a random sample of units for which transition times were successfully detected and validated (see Methods), time-locked to the wave shown in A. U-D and D-U transition times for each unit are indicated by circles and squares, respectively. The standard deviation of transition times across all validated units indicates the degree of synchrony of the transitions for this wave. C: Distribution across all the 50% largest waves (N = 47) of the standard deviation across units of the validated transition times. U-D transitions are more synchronous than D-U transitions (p < 0.001, Wilcoxon signed-rank test). This was the case for all the tested sets of parameters used to detect transition times (p < 0.001 for all N = 1024 parameter combinations; see S4 Fig).

Fig 8.. Local dependence of slow activity on synaptic weights.

Slow activity in the sleep (A) or wake (B) mode following local scaling of PyCs and BaCs peak AMPA conductances ($g_{pea{k}_{AMPA}}$). We modified AMPA conductances in the subnetwork illustrated by a red square and measured activity from units situated either locally (subnetwork 1) or in a subnetwork distant from the modulated zone (subnetwork 2). Reference sleep and wake mode simulations are marked by the red triangles. We performed 30 s simulations for all parameter values. A-1, B-1: SWA (0.5 – 2 Hz). A-2, B-2: Frequency of occurrence of above-threshold waves.

Fig 9.. Network stimulation can elicit large, synchronous slow waves in both the wake and sleep modes.

In both the spontaneous wake and sleep modes, we repeatedly stimulated a random sample of 25% of either all units or MaCs only with DC pulses of varying amplitudes. A: Overall network LFP time course locked to the stimulation pulse, for a single pulse of different amplitudes. Circles indicate the LFP value 200 ms post-stimulation. Stronger stimulation leads to a spike-and-wave pattern similar to that obtained with cortical stimulation in vivo. B: Boxplots of the LFP amplitude 200 msec post-stimulation, used as a proxy to measure the amplitude of the evoked wave, for all values of the pulse amplitude. We simulated N = 20 (“wake”) or N = 30 (“sleep”) trials for each pulse amplitude. The red line represents the threshold for wave detection used throughout. Network stimulation can evoke waves largely above detection threshold that are synchronized across the whole network.